论文信息 - Aperiodicity determinants expressed in terms of roots

Aperiodicity determinants expressed in terms of roots

In known set of necessary and sufficient conditions for a linear system to be aperiodic, certain determinants are required to be positive. In the present paper these determinants are represented as sums of products of squares of root-pair-differences. The historical background of this result in nineteenth-century algebra is explored. Criteria are also obtained for roots to be all real without being necessarily simple.

A. T. Fuller | A. Fuller

[1] C. Jacobi. De formatione et proprietatibus Determinatium. , 1841 .

[2] V. V. Krishnan,et al. Inners and Stability of Dynamic Systems , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[3] W. Burnside,et al. Theory of equations , 1886 .

[4] Peter Lancaster,et al. The theory of matrices , 1969 .

[5] A. Fuller,et al. Conditions for aperiodicity in linear systems , 1955 .

[6] Alston S. Householder,et al. Bigradients and the Problem of Routh and Hurwitz , 1968 .

[7] T. Muir. The Theory of Determinants in the Historical Order of Development , 1920 .

[8] Algebraische untersuchungen in Italien, 1850–1863 , 1980 .

[9] Joseph Miller Thomas. Sturm's Theorem for Multiple Roots , 1941 .

[10] A. Talbot. The Number of Zeros of a Polynomial in a Half-Plane , 1960, Mathematical Proceedings of the Cambridge Philosophical Society.

[11] Peter Henrici,et al. Constructive aspects of the fundamental theorem of algebra : proceedings of a symposium conducted at the IBM Research Laboratory, Zürich-Rüschlikon, Switzerland, June 5-7, 1967 , 1972 .

[12] M. Bôcher. Introduction to higher algebra , 2013 .